How Digital Clock Works

A source of power to run the clock
In a pendulum clock, the weights or the springs handle this role.
An accurate timebase that acts as the clock's heartbeat
In a pendulum clock, the pendulum and escapement handle this role.
A way to gear down the timebase to extract different components of time (hours, minutes, seconds)
In a pendulum clock, gears serve this role.
A way to display the time
In a pendulum clock, the hands and face serve this role.

A digital clock is no different. It simply handles these functions electronically rather than mechanically. So in a digital clock, there is an electrical power supply (either a battery or 120-volt AC power from the wall). There is an electronic timebase that "ticks" at some known and accurate rate. There is an electronic "gearing mechanism" of some sort -- generally a digital clock handles gearing with a component called a "counter." And there is a display, usually either LEDs (light emitting diodes) or an LCD (liquid crystal display).